I have received several answers to my question. Thanks to everyone who
responded.
David explained:
Plot[2 x - 3 (x^2)^(1/3) + 4, {x, -1, 6}]
Note that, for negative x, x^(2/3) and (x^2)^(1/3) are not the same in
Mathematica.
The latter expression gives a positive value, which is what you want,
while the former expression gives the _principal_ value of the 2/3
power, which has a nonzero imaginary part and so does not plot.